Effects of $A_t$ and $μ$ phases on B and K physics in the effective supersymmetric models

Abstract

In the minimal supersymmetric standard model (MSSM), the $μ-$parameter and the trilinear coupling $A_t$ may be generically complex and can affect various observables at B factories. Working in the effective SUSY models and imposing the edm constraints from Chang-Keung-Pilaftsis (CKP) mechanism, we find that (i) there is no new large phase shift in the $B^0 - \bar{B^0}$ mixing from the A_t and $μ$ phases, (ii) CP violating dilepton asymmetry is smaller than 0.1%, (iii) the direct CP violation in $B\to X_s γ$ can be as large as $\sim \pm 16 %$, (iv) the ${\rm Br} (B\to X_s l^+ l^-)$ can be enhanced by upto $\sim 85 %$ compared to the standard model (SM) prediction, and its correlation with ${\rm Br} (B \to X_s γ)$ is distinctly different from the minimal supergravity scenario. Also, we find $1 \leq ε_K / ε_K^{SM} \leq 1.4$, and $ε_K$ cannot be saturated by the A_t and $μ$ phases alone : namely, $|ε_K^{\rm SUSY}| \leq O(10^{-5})$ if the phases of $μ$ and A_t are the sole origin of CP violation.